The Impact of R5 on Req Calculation

[mabdeljaber]

Homework Statement

Consider the circuit to the right, with R5 = 119 Ω in series with the capacitor. Once again, the switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

Relevant Equations

I=V/R , Req=R235+R14

So what I know is that without the edition of the R5 resistor R2 and R3 are 0 because the capacitor is short circuiting them. Why does the addition of the R5 resistor cause R2 and R3 to be calculated into the Req for the current equation?

 

[kuruman]

Adding R₅ makes a difference because R₂ and R₃ are no longer shorted. Redraw the circuit with the capacitor as a "short" to find the initial R_eq and hence the initial current through R₁ the usual way.

 

[mabdeljaber]

Adding R₅ makes a difference because R₂ and R₃ are no longer shorted. Redraw the circuit with the capacitor as a "short" to find the initial R_eq and hence the initial current through R₁ the usual way.

Thank you I kind of understand that, but how do I redraw the circuit with the capacitor as a "short". I don't really understand what that looks like

 

[gneill]

Thank you I kind of understand that, but how do I redraw the circuit with the capacitor as a "short". I don't really understand what that looks like

Replace the capacitor with a wire.

 

[mabdeljaber]

Replace the capacitor with a wire.

Thank you! Understood

 

[Delta2]

Maybe we have to explain why the capacitor at time t=0 behaves as a short. The reason is that the capacitor is assumed to be uncharged so its voltage is zero at this time instant. So if you apply KVL for the time instant t=0 you ll see that the resulting equation is like that the capacitor is a short.

If the capacitor had some initial charge or if we were asked for the current at another time instant then you shouldn't replace the capacitor with a short. You will had to solve differential equations then (unless the charge of the capacitor at that time instant was given).